Thursday, December 03, 2015
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Steve Hsu has made a hostile comment about the Copenhagen interpretation and I decided to write a specific blog post about the history of the term and how the meaning got distorted to describe something that physicists may call controversial – which they may not.

The #1 discoverer of quantum mechanics as a new framework of physics based on linear operators – in the form of "matrix mechanics" – was Werner Heisenberg who made the crucial realizations in 1925. He left for the Heligoland island on June 7th to escape hay fever and that was a great place for big discoveries.

Heisenberg wrote an important early paper with Jordan and Born. In the 1920s, he was employed by Bohr in Copenhagen. Bohr was this revolutionary generation's guru. He did some "preliminary steps" to understand the atom in 1911 – his planetary model – and he was the main older guy who was willing to crack the problem completely. He was a good listener – so he listened to all these very bright younger folks. They (guys in their 20s) must have liked it and needed an older father-like figure like that but I think it's obvious that most of the "new" quantum mechanics was found by the people born between 1900 and 1902, the young big shots. Bohr still deserves much of the credit for quantum mechanics and its foundations in the same sense in which Steve Jobs deserves some credit for the iPhone.

They would know how to calculate things in practice but may have been confused why it worked and what the exact rules actually are. It is obvious that these doubts have evaporated by 1927 when the conventional postulates of quantum mechanics were fully postulated. It was the same year when Heisenberg articulated the "uncertainty principle" clearly. Heisenberg and Bohr would discuss things intensely at those times. Bohr would emphasize "complementarity". The noncommuting character of the observables meant that there are many "angles" from which you may think about (observe) a given physical system.

In 1927, they must have decided that what they were saying was equivalent. Bohr's views may have been vague which allowed them to see that "within the error margin", they were saying the same things. But I am totally convinced that the interactions with Bohr and Bohr's contributions were crucial for the right philosophical mood of the founding fathers of quantum mechanics and Heisenberg in particular – and to understand what was exactly going on.

But in that year 1927, the term "Copenhagen interpretation" wasn't born yet. When did it emerge? Wikipedia gives us an answer. The originator wasn't Bohr himself – it would be too narcissistic a piece of history. The term "Copenhagen interpretation" evolved from Heisenberg's words that were meant as thanks to Bohr and his role as the boss of the environment in Denmark that allowed physics to advance so incredibly dramatically in such a short period of time.

In 1929, Heisenberg gave lectures at the University of Chicago and they were published in a written form as

The capital of Denmark has played the role of an emerging jargon in the preface written by Heisenberg himself:

...On the whole the book contains nothing that is not to be found in previous publications, particularly in the investigations of Bohr. The purpose of the book seems to me to be fulfilled if it contributes somewhat to the diffusion of that 'Kopenhagener Geist der Quantentheorie' [i.e., Copenhagen spirit of quantum theory] if I may so express myself, which has directed the entire development of modern atomic physics.

He credits Bohr with those advances although it's not easy to find Bohr's texts that would be as clear as the lectures by Dirac, Heisenberg, or others. And the term he coined was "Kopenhagener Geist der Quantentheorie". "Geist" is a ghost, like in Zeitgeist or Poltergeist, so they translated the sequence of German words as the "Copenhagen spirit of quantum theory" even though they kept the original in the English translation, too.

It's not too usual for names of such cities to appear in such contexts so you may be pretty sure that this early phrase was the reason why the "Copenhagen interpretation" has spread so much later. It cannot be a coincidence. But with the word "interpretation", the phrase began to be used only in the 1950s. I believe that even in the new form, it was coined by Heisenberg, but I haven't traced the very first sources etc.

I think he was the first man who combined the words "Copenhagen" and "interpretation" but he only included the word "interpretation" because others – who misunderstood quantum mechanics 24 hours a day or at least during a part of the day (like David Bohm) – have used the word before him. Heisenberg adopted the word "interpretation" only when new "variations" of the rules what to do with the mathematical objects in quantum mechanics were available on the market. Lectures with the titles The Copenhagen Interpretation of Quantum Theory (some kind of intro to quantum mechanics) and Criticisms and Counterproposals to the Copenhagen Interpretation (a wonderfully vigorous response to the anti-quantum zealots of the 1950s, see the bottom of the blog post) that Heisenberg delivered in 1955 were reprinted in the collection Physics and Philosophy (click for full PDF). Before the book was out, Heisenberg said he was sorry for the choice of the title because it suggested that there could be "other interpretations" even though what those other people were saying about quantum mechanics was just nonsense.

"I avow that the term ‘Copenhagen interpretation’ is not happy since it could suggest that there are other interpretations, like Bohm assumes. We agree, of course, that the other interpretations are nonsense, and I believe that this is clear in my book, and in previous papers. Anyway, I cannot now, unfortunately, change the book since the printing began enough time ago."

In 1955, before the book was out, he already suspected that the phrase "Copenhagen interpretation" would encourage the proliferation of cranks and boy, he was unfortunately so right.

(As this thesis says, the term and its content was mostly invented by Heisenberg but it only became widespread once Bohm, Feyerabend, Hanson, and Popper, among others, began to use the term in their own, often twisted, wrong, and off-topic, essays.)

What seems more important to me is what the "Copenhagen spirit" meant back in 1929 or 1930. Heisenberg makes it clear that it wasn't some explicit, optional philosophical essay retroactively explaining "what the hell we were actually doing when we were working with quantum mechanics in the past" which is how the term "Copenhagen interpretation" is often presented today.

Instead, the "Copenhagen spirit" was the essential "way of thinking" that the founders needed to adopt when they were discovering the new foundations of physics; and the way of thinking that the people attending Heisenberg's lectures (or others) had to embrace if they wanted to understand the new rules of physics. The word "spirit" sounds much more vague than an "interpretation". It doesn't mean that quantum mechanics is vague. Quantum mechanics has extremely well-defined rules and they're outlined in the textbooks by Dirac, Heisenberg, and others.

But one can't understand let alone discover the new rules if his broad way of thinking about the Universe is wrong. So he has to adopt the right spirit first. Once you are infused with the right Copenhagen spirit, you only need some technicalities and hard work to comprehend the new theory. But without the right spirit, you may be in a hopeless situation.

So the whole chronology or causality that the "interpreters" associate with the "Copenhagen interpretation" these days is just completely wrong. They pretend that it's some addition to the mathematical rules of quantum mechanics, an addition that has competitors and you may choose in between them. But what Heisenberg meant was something entirely different. Physics is about theories, not controversial philosophical essays, and they surely had the unique right theory by the end of the 1920s. But the new theory is conceptually different from the old, classical physics, which is why it may be hard to understand it. And that's why one needs the Copenhagen spirit first.

The Copenhagen spirit is a prerequisite to understand quantum mechanics but once one gets to the point of understanding quantum mechanics in detail, he gets the full picture and the way how one got there becomes less important and there's no room for additional "interpretations". That's why all the criticisms complaining the the "Copenhagen interpretation isn't sharply defined anywhere" are completely missing the point.

For example, Wikipedia says

According to an "opponent" of the Copenhagen interpretation, crackpot John G. Cramer, "Despite an extensive literature which refers to, discusses, and criticizes the Copenhagen interpretation of quantum mechanics, nowhere does there seem to be any concise statement which defines the full Copenhagen interpretation."

It's because there is nothing quantitative in physics that should be called the Copenhagen interpretation. There is nothing to "interpret" about quantum mechanics within itself. As Sidney Coleman pointed out, if something should be interpreted within quantum mechanics, it is classical physics (a limit), not quantum mechanics. Instead, what physics contains is something that should be called the theory of quantum mechanics. The Copenhagen interpretation is a way of thinking, heuristic ideas, or isolated novelties one has to get familiar with before he understands the theory in detail. But physics contains the well-defined and complete theory, quantum mechanics, and nothing else can be or has to be added on top of that. "The universal postulates of quantum mechanics" are the precise set of rules that refine what is popularly referred to as the Copenhagen interpretation!

But there exists a complete theory – indeed, the relationship between the mathematical objects and the experimentally measured quantities is an important part of this theory – and it's just plain wrong to suggest that something is missing or has to be added on top of the theory. There is nothing to be interpreted.

Glenn Miller's "In The Mood" was the most popular song of the 1930s.

The 200-page 1930 book by Heisenberg is a very nice and coherent reading. I recommend it. It was written just 5 years (and taught 4 years) after Heisenberg saw the "relevant mathematics" to understand atomic physics for the first time. But like Dirac's early textbook and others, it already looks like an authoritative description of a settled subject. It is way more coherent than virtually every contemporary article talking about "interpretations" of quantum mechanics – despite the fact that we have already had 90 years to sort all these ideas.

In Chapter 1, Heisenberg says that things would be easy if people were just talking about their observations. The conceptual difficulties begin when they start to build theories explaining these observations. Such theories generically involve some generalizations of our actual observations, and those extrapolations may go and often do go too far.

So ideally, one would eliminate all assumptions from the theory that can't be backed by actual evidence. In practice, we wouldn't get anywhere in this way. So theories do have to assume the existence of some concepts. But we must be at least ready to retire them if they run into problems, into tension between theory and experiments.

He explicitly spells the analogy between the philosophical lessons of relativity and philosophical lessons of quantum mechanics. In special relativity, there are no infinitely fast signals and things really seem to look new near the speed of light so one has to abandon the idealized, observer-independent notions of simultaneity, measuring rods, and clocks. We know that they can be kept only if we specify the inertial system carefully. Similarly, Newtonian concepts must be even more deeply revised in general relativity.

Quantum mechanics is analogous but its required revision of concepts is even deeper. The concept of "observation" had been used with the implicit assumption that it could have been done so that it didn't affect the measured system. But this assumption wasn't justified by any evidence so we must be open-minded and admit that it may be wrong. And indeed, the new viable theory tells us quite some details about the fact that the observation unavoidably influences the measured system. It also means that if we measure one thing and then second thing, the knowledge from the first measurement may in principle be rendered obsolete thanks to the changes caused by the second measurement. And yes, that's what's happening because of the uncertainty principle.

At the end, the most general "metaphysical" lesson that Heisenberg stresses – and that he had to appreciate when he was converging to quantum mechanics – is the lesson that the human language etc. (which was developed to describe a limited spectrum of phenomena) may impose lots of hidden assumptions on us, assumptions that are not justified by the (ultimately empirical) evidence and that may be wrong. And we have to be ready to throw away these assumptions and revise the meaning of all the concepts we are using.

That's how Heisenberg "frames" both relativity and quantum mechanics: both of them arise from a similar "critique" of unjustified and ultimately invalid assumptions hiding behind the language of the old theory.

In the rest of Chapter 1, Heisenberg discusses some experiments proving both corpuscular and wave properties of particles and light. But he is getting ready for Chapters 2 and 3 which are called "critiques". In Chapter 2, his critique focuses on the classical theory of particles; in Chapter 3, it concentrates on the classical theory of waves. He shows the actual experimental problems that emerge if you want to measure the positions or velocities too accurately and gives an "experimenter's" proof of the uncertainty principle in various ways as well as a mathematical proof. There are similar discussions about the wave and field measurements.

Chapter 4 is about the statistical interpretation of the amplitudes. Clearly, in this context, no sane person would suggest that the word "interpretation" means that there are many alternatives. The word just means that we need to connect the complex amplitudes with things from the experimenter's life – and they clearly have to be probability amplitudes. Sections are about the mathematical rules for probabilities; interference; and Bohr's complementarity. The following Chapter 5 describes many experiments in detail while the Appendix summarizes all the mathematically-loaded parts of quantum mechanics.

He doesn't avoid the wave function. It just doesn't play the "pioneering" role as it does in many unfortunate contemporary texts. He derives all the "authority and truth" in physics from the experiments and observations, operationally doable things. We can't measure the wave function. It's really very far from the experiments we are making and it is very obvious that the people who place the wave function at the center of their thinking are very far from the point that the concepts and laws of physics must ultimately be supported by empirical arguments.

Instead, Heisenberg stays focused on the observables like \(x,p\) – which are represented by linear operators in quantum mechanics.

Quantum mechanics destroys many assumptions of classical physics - e.g. the assumption that the position and velocity simultaneously exist with any accuracy. But it may be equally important to know that quantum mechanics really keeps some things, too. So it is still fully appropriate to exactly describe the behavior of a particle by \(x\) and \(p\). Those may be experimentally measured etc. They just have different properties and the measurements have to be predicted totally differently than in classical physics!

In the misguided pedagogical approaches that create kilotons of new anti-quantum zealots, the students are led to throw the baby out with the bath water. They are led to believe that "there is no \(x\)" and "there is no \(p\)" anymore – and those things in classical physics are replaced by the wave function. This sounds analogous to the way how classical mechanics was superseded by classical field theory (e.g. Maxwell's theory) so the students are encouraged to think that it's not a big deal. Quantum mechanics is just a new kind of a classical theory. They don't use the adjective "classical" but they mean it. They say "quantum" but what they actually believe that the word means is "some more complicated classical model". They still believe that the theory is qualitatively the same and it has some classical objective degrees of freedom, just different ones represented by a function with many more dimensions. So most of these people never understand quantum mechanics at all.

The reality – as presented by Heisenberg – is different. \(x\) and \(p\) are meaningless when you try to make both of them too accurate. But in separation, they are still OK and mechanics is still built upon them because those are the things that we know how to measure (and the measurements seem like the simplest ones, so they are concepts that physics simply cannot ignore). So the transition from classical physics to quantum mechanics isn't a transition from \(x(t)\) and \(p(t)\) to \(\psi(x,y,z,t)\). Instead, it is a transition from the classical \(c\)-number-valued \(x\) and \(p\) to the \(x\) and \(p\) with the new properties – the noncommuting operators. We're basically measuring the same things as we did but we must be more careful what it means if we measured something and what it allows us to predict – and how the predictions are made.

Most fields of the human activity have seen persistent progress. But it's remarkable to see how much negative progress has occurred in the recent 85 if not 90 years in the field of "writing about the foundations of quantum mechanics". In 1930, people had folks like Heisenberg who had actually discovered the totally new foundations of physics, knew how to avoid all the traps and possible mistakes, and what they were, and they just presented the new theory in the no-nonsense way. Today we have tons of Deutsches, Wallaces, Puseys, Rudolphs, Barretts, Hsus who are sloppy all the time, who are dogmatic about things that are unsupported or directly contradict the evidence, and who are deliberately obfuscating some points in order to mask the incoherence of their message and indefensibility of the claim that quantum mechanics needs an "addition" and the universal postulates of quantum mechanics that materialized out of the Copenhagen spirit have to be replaced by one of their incoherent new sloppy irrational pictures that are designed to return physics to the era of classical physics, a goal that obviously can never succeed.

P.S.: Lots of texts, e.g. Howard's thesis and the Stanford philosophers, claim that there was some big disagreement between Heisenberg and Bohr etc. Bohr didn't believe that the wave function collapsed or that it was subjective etc. This is just a pile of rubbish. First of all, Bohr knew that Heisenberg was younger and sharper so whatever they agreed with, and they did basically agreed to agree, Heisenberg was going to express more meaningfully. So Bohr always supported Heisenberg. That's a sociological point. But the other point is that Bohr's complementarity from the 1920s was about the different perspectives from which objects may be observed. It included the in-principle difference and irreconcilability of the views of two observers. Bohr surely helped to realize those things; it's silly to say that he disagreed with them. It's also silly to claim that he didn't "agree" that the wave function collapses in any way. It does collapse – a wave function that would spread indefinitely would clearly be experimentally falsified. What is subtle is the character of the collapse and they figured out that it has to be understood as a change of the observer's subjective knowledge – which is why it may abruptly change in distant corners of space without causing any superluminal signals. There exists no alternative way to describe any of these things. Bohr hasn't been too clear but he did endorse all those things by endorsing Heisenberg's views as a whole. Even if he didn't, it wouldn't matter. It would still be true that Heisenberg's interpretation – or its decorated variations – is the only one that makes any sense.

Bonus

I read a part of the 1955 Heisenberg essays on the Copenhagen Interpretation (which coined the unfortunate term) and they're wonderful. To lure you, here's a beginning of the "Criticism and Counterproposals" essay (the full PDF is linked to above):

The Copenhagen interpretation of quantum theory has led the physicists far away from the simple materialistic views that prevailed in the natural science of the nineteenth century. Since these views had not only been intrinsically connected with natural science of that period but had also found a systematic analysis in some philosophic systems and had penetrated deeply into the mind even of the common men on the street, it can be well understood that many attempts have been made to criticize the Copenhagen interpretation and to replace it by one more in line with the concepts of classical physics or materialistic philosophy.

These attempts can be divided into three different groups. The first group does not want to change the Copenhagen interpretation so far as predictions of experimental results are concerned; but it tries to change the language of this interpretation in order to get a closer resemblance to classical physics. In other words, it tries to change the philosophy without changing the physics. Some papers of this first group restrict their agreement with the experimental predictions of the Copenhagen interpretation to all those experiments that have hitherto been carried out or that belong to normal electronic physics.

The second group realizes that the Copenhagen interpretation is the only adequate one, if the experimental results agree everywhere with the predictions of this interpretation. Therefore, the papers of this group try to change quantum theory to some extent in certain critical points. The third group, finally, expresses rather its general dissatisfaction with the results of the Copenhagen interpretation and especially with its philosophical conclusions, without making definite counterproposals. Papers by Einstein, von Laue and Schrodinger belong to this third group which has historically been the first of the three groups.

However, all the opponents of the Copenhagen interpretation do agree on one point. It would, in their view, be desirable to return to the reality concept of classical physics or, to use a more general philosophic term, to the ontology of materialism. They would prefer to come back to the idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them.

This, however, is impossible or at least not entirely possible because of the nature of the atomic phenomena, as has been discussed in some of the earlier chapters. It cannot be our task to formulate wishes as to how the atomic phenomena should be; our task can only be to understand them. When one analyzes the papers of the first group, it is important...

I've never read it before but it looks like The Reference Frame to me. ;-) How Heisenberg continues is innovative. It was before many specific theorems against hidden variables were proven but he dismissed the hidden variables as a repetition of his "interpretation", anyway. Bohm's theory is totally debunked starting from a cute observation by Pauli I never realized. (Note that Pauli's famous phrase "not even wrong" was voiced as a criticism against Bohm's alternative "interpretation".)

Pauli has pointed out that most atoms ground states should have electrons at fixed positions. This is easy to see: the velocity is zero simply because the wave function is real and the probability current vanishes. But when you actually measure the velocities, you never get zero. There's a particular distribution in which the velocity is always nonzero (the Fourier transform of the wave function gives you the wave function in the momentum space). So Bohm of course had to agree that his velocity of the "actual particle" \(d\vec x /dt\) has nothing to do with the velocity we may measure.

Bohm had to agree to "ban" the new Bohmian velocity that his "interpretation" was producing and accept Heisenberg's velocity extracted from the Born rule applied on the Fourier-transformed wave function. ;-) More generally, he is adding all this superstructure and whenever there is something new that should be observable according to his own realist rules and that would follow from this structure, he has to hide it, throw it away, declare it unobservable, and use the correct quantum mechanics instead. No one cares that it's this pathetic pile of feces and even now, in 2015, this rubbish has its advocates.

When Bohm expressed "hope" that violations of QM would be found later and hidden variables supported, Bohr responded that the strange sentence is almost isomorphic to "I hope that \(2\times 2=5\) will be proven at some point which will have a good effect on our finances." I think that I have independently used exactly the same metaphor as Bohr has! ;-) And there are lots of other sections nicely comparing the anti-quantum zealots with the critics of relativity etc. Some Russian critics of Copenhagen who want to keep the physics of Copenhagen but make the language materialistic are shown to be nothing else than blind disciples of Lenin's. :-)

Heisenberg's debunking of his contemporary crackpots is just sweet. He would probably have a great time today when the number of these lunacies has increased by orders of magnitude and most of them are way more idiotic than Bohm's was. But I suspect that he might get frustrated by the mankind's skyrocketing stupidity in the same way as I did.